Henry Winkler has done a lot of promotion for the series and films that mark his career spanning more than four decades, but seeing his face on a New York City subway ad for HBO’s “Barry” takes the cake.

“I have to tell you something,” Winkler says after finishing his lunch of soup, shrimp and “too much bread” on a Tuesday afternoon at the network’s offices. “I have been a professional since June 30, 1970, it is my favorite advertising campaign I think I have ever been a part of.”

The New Yorker whose claim to fame came in the form of the 1970s hit “Happy Days” is back on television as a Hollywood acting coach in “Barry.” To promote the dramedy, HBO plastered ads for classes with Winkler — in character as “Acting Teacher Extraordinaire” Gene M. Cousineau — in buses and subway cars in Manhattan this spring.

“If you call the number (818-NEW-STAR), I talk to you. I recorded it on my telephone, I can do this,” Winkler, 72, says grabbing his iPhone to demonstrate.

“I recorded on whatever it’s called and sent it to HBO on email and presto, bingo I’m on bus stops! It was amazing. I’m very proud,” the actor, offsetting a blue blazer with a spring yellow tie, explains.

Winkler is also incredibly proud of his stint as the fictional acting teacher in general. With scattered roles on “Arrested Development,” “Parks and Recreation,” “New Girl” and other sitcoms, the recurring HBO gig just might be his current-day “big break.”

“I was 27 when I thought I really knew what I’d like to be as an actor, and I’m now 72,” he explains. “I’ve flipped the numbers and I am just now coming out of the cocoon. Maybe I’m better than I’ve ever been.”

The role of Gene — the mentor to a group of struggling wannabe stage and TV actors who are joined by Barry, a hit man in disguise played by “SNL” alum Bill Hader — was “so sought after” in Hollywood, Winkler notes. His character adds necessary comic relief to a show that somehow manages to balance gruesome death scenes with an at times absurd acting class.

“Oh my god, (Gene) brings back the reality of my acting classes. I’ve had some great ones and some that I didn’t know what they were doing,” Winkler says. “I just conglomerated them and out came Gene.”

Henry Winkler's latest TV role in HBO's "Barry" just might be his best, he says. Photo Credit: HBO / John P. Johnson

The actor’s own journey to break into the industry in the early ‘70s in New York City ended up crafting parts of the script.

One class prompt in particular that sees Winkler instruct Barry (Hader) to imagine he’s walking the class down a grocery store aisle was lifted from an experience with a teacher from his past.

Studying drama at Yale, Winkler was in his freshman year when he met famed acting teacher Stella Adler.

“She had her dog with her, some small thing. Her tongue would come out of her mouth and the dog’s tongue would come out of his mouth,” he jokes.

He continues, “Stella, she would say, ‘I want you to create a garden in your mind and let us see it. I stand up, I open the imaginary picket fence and say, ‘Here are the …’ ‘SIT DOWN. You see nothing,’ she said.”

Winkler notes it was reflecting back on moments like this that drew him to the role, relating fondly to Gene’s group of struggling students. Before landing his “Happy Days” role, Winkler spent time doing commercials in New York City — something he notes his acting class peers dubbed as the work of a traitor to the trade.

“I thought commercials were the best thing since sliced bread, but I couldn’t get a play for all the tea in China,” he recalls. “Finally, in March of 1973, I opened and closed in one night on Broadway. It was called '42 Seconds From Broadway,' and I think the title was longer than the run.”

“And then, in September of that year, I went to California with one month’s amount of money — $1,000 I saved from commercials — two weeks later I got The Fonz. Amazing.”

Though now 34 years removed from “Happy Days,” a deep appreciation for the experience keeps Winkler connected to the iconic role even while portraying a character vastly different.

“I am grateful. My joke is, you know how wonderfully supportive The Fonz is? He watches ‘Barry,’” Winkler says straight-faced. “Isn’t he nice? Yes. We built a small little house for him on our property and he helps to fix our cars.”

“Barry” fans — including The Fonz — watch the series Sunday nights at 10:30 p.m. on HBO. You can catch up now for free at HBO.com/Barry.